Floating Point Arithmetic Issues & Limitations

Notes from Chap. 15 of the official Python tutorial, Floating Point Arithmetic: Issues and Limitations

Base 2 (binary system) - numbers are expressed using only two symbols, typically 0 and 1.
Base 2 fractions - fractions in one base (e.g. base 10) can be converted to another base (e.g. base 2) using several methods.
Base 10 (decimal system) - numbers are represented with 10 symbols (e.g. arabic numerals) and a separator (e.g. a dot).
Base 16 (hexadecimal system) - numbers are represented with 16 symbols, most commonly 0-9 for zero to nine and A-F for ten to fifteen
Bit - binary digit (e.g. 0 or 1)
Floating point numbers - numbers with decimal points. (INCOMPLETE FOR NOW.)

Floating point numbers are represented in computer hardware as base 2 (binary) fractions
Representation error: Most decimal fractions can’t be represented exactly as binary (base 2) fractions

Python (and other programming languages) often won’t display the exact decimal number one expects

Use the fractions and decimal modules to make calcuations between floats, fractions & decimals
The round() function can be useful for post-calculation rounding so that inexact values become comparable
Look at SciPy if doing a lot of floating point operations
There are tools that can be used to get the exact value of a float (float.as_integer_ratio(), float.from_hex(), math.fsum()